Answer:
Option A. The volume of the sphere is multiplied by 1/343.
Step-by-step explanation:
The volume of a sphere can be obtained by the following formula:
V = 4/3πr^3
Let the initial volume (V1) of the sphere be:
V1 = 4/3πr^3 = (4πr^3)/3
Now, if we multiply the radius by 1/7, then the new volume (V2) of the sphere will be:
V2 = 4/3 x π x (1/7r)^3
V2 = 4/3 x π x 1/343r^3
V2 = (4πr^3)/1029
Now we determine the ratio of V2 : V1 as shown below:
V2/V1 = (4πr^3)/1029 ÷ (4πr^3)/3
V2/V1 = (4πr^3)/1029 × 3/(4πr^3)
V2/V1 = 3/1029
V2/V1 = 1/343
V2 = 1/343 x V1
Therefore, the volume of the sphere is multiplied by 1/343.
3 dozen = 36
1/3 ÷ x = 5 ÷ 36
1/3 × 36 = x × 5
12 = 5x
12/5 = x
12/5 cups of flour is needed
C because it makes complete common sense but idk though just in case I'm wrong and u can't blame me lol
Simplifying
8a + 12b = 92
Solving
8a + 12b = 92
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-12b' to each side of the equation.
8a + 12b + -12b = 92 + -12b
Combine like terms: 12b + -12b = 0
8a + 0 = 92 + -12b
8a = 92 + -12b
Divide each side by '8'.
a = 11.5 + -1.5b
Simplifying
a = 11.5 + -1.5b
Let's take two different equations.
4x+2y=8
7x+3y=-10
(I just came up with these on the spot, so the answers might be strange but i should be able to explain nevertheless)
First, let's solve the first equation for "y".
4x+2y=8
-4x -4x
2y=8-4x
/2
y=4-2x
Now that we have "y", let's plug it into the second equation.
7x+3(4-2x)=-10
7x+12-6x=-10
x+12=-10
-12 -12
x=-22
Alright, now we have "x" definitively, let's plug it in to find "y".
4(-22)+2y=8
-88+2y=8
+88 +88
2y=96
/2
y=48
So from this example you can see. You solve one variable in terms of another (solve y as being 4-2x), plug it into the second equation to find one variable's value, then plug that variable's value back in again later to get the first variable's value.
